The two-dimensional kinetic model of the scrape-off layer recently suggested by Catto and Hazeltine [Phys. Plasmas 1, 1882 (1994)] is extended by allowing for ion recycling at the limiter or divertor plates by an effective ion reflection coefficient. The model describes the balance between radial diffusion and streaming along the magnetic field, and the structure of the resulting scrape-off layer is found to depend on the reflection coefficient. The particle and heat loads on the limiter or divertor plates are calculated, as well as the boundary conditions on the density and temperature gradients of the core plasma. By assuming that electrons have a Maxwell-Boltzmann distribution, the radial variation of the plasma potential is determined, and the potential of the Debye sheaths formed at the limiter or divertor plates is estimated.